Fig. 5 shows the temperature \(T\) , the density \(\rho \) , and the Mach number on the equatorial plane in model Thick5, where
a spike-like feature of the temperature across the shock front is found, differently from
the discontinuous front in the optically thin models AD and Thin1.
Under consideration of the radiation heat conduction and the supercritical shock wave,
[1]} estimates the optical thickness \(\Delta \tau _{\rm s}\)  of the shock region as,
\(\Delta \tau _{\rm s} = {4 \over {3\surd {3}}} \left[ \left({T_{-} \over T_{\rm c}}\right)^3 -1\right] ,\) 
